Noncommutative descent and non-Abelian cohomology

被引：27

作者：

Nuss, P

机构：

[1] UNIV STRASBOURG 1,INST RECH MATH AVANCEE,F-67084 STRASBOURG,FRANCE

[2] CNRS,F-67084 STRASBOURG,FRANCE

来源：

K-THEORY | 1997年 / 12卷 / 01期

关键词：

descent; braid equation; connection; Hopf-Galois extension; non-Abelian cohomology; Hermitian module; Hilbert's Theorem 90;

D O I：

10.1023/A:1007734431772

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the descent problem of modules over general extensions of noncommutative rings and give different interpretations of descent data. We consider in particular the case of Hopf-Galois extensions. When descent data exist, we classify them by non-Abelian cohomology sets and deduce a noncommutative version of Hilbert's Theorem 90.

引用

页码：23 / 74

页数：52

共 50 条

[31] Construction of non-Abelian gauge theories on noncommutative spaces
B. Jurčo
L. Möller
S. Schraml
P. Schupp
J. Wess
The European Physical Journal C - Particles and Fields, 2001, 21 : 383 - 388
[32] ALMOST SHORT EXACT SEQUENCES IN NON-ABELIAN COHOMOLOGY
IGODT, P
JOURNAL OF PURE AND APPLIED ALGEBRA, 1986, 41 (01) : 51 - 61
[33] Categorical non-abelian cohomology and the Schreier theory of groupoids
V. Blanco
M. Bullejos
E. Faro
Mathematische Zeitschrift, 2005, 251 : 41 - 59
[34] Non-abelian Hopf cohomology II - The general case
Nuss, Philippe
Wambst, Marc
JOURNAL OF ALGEBRA, 2008, 319 (11) : 4621 - 4645
[35] Syzygies in Equivariant Cohomology for Non-abelian Lie Groups
Franz, Matthias
CONFIGURATION SPACES: GEOMETRY, TOPOLOGY AND REPRESENTATION THEORY, 2016, 14 : 325 - 360
[36] Low-dimensional non-abelian Leibniz cohomology
Manuel Casas, Jose
Khmaladze, Emzar
Ladra, Manuel
FORUM MATHEMATICUM, 2013, 25 (03) : 443 - 469
[37] NON-ABELIAN COHOMOLOGY OF UNIVERSAL CURVES IN POSITIVE CHARACTERISTIC
Watanabe, Tatsunari
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (01) : 89 - 103
[38] Categorical non-abelian cohomology and the Schreier theory of groupoids
Blanco, V
Bullejos, M
Faro, E
MATHEMATISCHE ZEITSCHRIFT, 2005, 251 (01) : 41 - 59
[39] NON-ABELIAN COHOMOLOGY A LA GIRAUD - PRELIMINARY REPORT
DIACONESCU, R
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (06): : A676 - A676
[40] AN EXACT SEQUENCE IN THE 1ST VARIABLE FOR NON-ABELIAN COHOMOLOGY IN ALGEBRAIC CATEGORIES - A MAYER-VIETORIS SEQUENCE FOR NON-ABELIAN COHOMOLOGY OF GROUPS
CEGARRA, AM
GARZON, AR
CARRASCO, P
LECTURE NOTES IN MATHEMATICS, 1988, 1348 : 72 - 86

← 1 2 3 4 5 →